Double reduction of PDEs from the association of symmetries with conservation laws with applications

摘要

We use the definition of the association of symmetries of partial differential equations with conservation laws [A. Kara, F. Mahomed, The relationship between symmetries and conservation laws, Int. J. Theor. Phys. 39 (1) (2000) 23–40] to find a double reduction of partial differential equations with two independent variables. Applications to the linear heat equation, the BBM equation, the sine-Gordon equation and a system of differential equations from one dimensional gas dynamics illustrate the new theory.